adapt to the depleted pump power and maintain
the optimal pump-signal frequency separation:
W~

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Pðz Þ=rðz Þ

p

¼ constant, where r(z) represents a unique core variation function. This
simple model, while establishing the need for
local core control, is also inaccurate because it
does not account for the higher-order mixing
products generated in efficient FPM interaction (13). To describe such a many-beam photon exchange in a spatially varying nonlinear
waveguide, it is necessary to use the nonlinear
Schrodinger (NLS) model (13).

The NLS model indeed predicts the existence
of an optimum core fluctuation (Fig. 2C). The
extinction ratio (ER), defined as the ratio of the
output pump power in the absence of the input
signal to the output pump power in the presence
of the input signal, was calculated for a fiber ensemble with randomly generated core variations.
Similar to physical fibers (12), ensemble members differed at the nanometer scale: Each had
unique local dispersion defined by random core
variations and limited by standard deviation s
below 5 nm. To illustrate this important notion,
consider two fibers that are identical in terms of
global parameters but also possess the same
standard core variation s = 2.2 nm (Fig. 2C,
inset). Although macroscopically indistinguishable,
the two samples possess drastically different
switching performance. In the first sample, a
300-nW signal depletes a 4.5 × 106 times
stronger (1.39 W) beam efficiently (ER = 12.3 dB),
with no effect in the second sample (ER = 0.3 dB).
This extreme sensitivity to core fluctuations is
even more remarkable when viewed in the context of glass structure: Its basic building block,
the Si-O molecular ring, has a 0.6-nm diameter
(16) and defines the ultimate precision with
which physical fiber core can be realized. Unfortunately, Fig. 2C implies that even if one succeeds in fabricating fiber with molecular-scale
transverse precision (∼1 nm), this would still
not guarantee the ability to build a few-photon
switch. Facing this fundamental limit, it would
appear that few-photon control in silica fiber is
not feasible, even in principle. However, recent
progress made in fiber measurement now allows
both core selection (18) and synthesis (19) with
subnanometer precision.

Although the localized stress technique cangenerate an arbitrary core variation profile (19),it can also perturb the native birefringence of thefiber. We therefore avoided this path in order todecouple the stochastic dispersion from any in-duced polarization effects. The fabrication-imposedlimit was instead circumvented by selecting spe-cific fiber segments with the desired core variation.Following this idea, it is necessary to first measure,with subnanometer precision, a fiber that is muchlonger than the switching device length. The abilityto perform such a measurement in a nondestruc-tive manner and over a long scale was establishedby a countercolliding Brillouin scanning technique(18). First, kilometers of fiber samples were mea-sured and core variations were recorded to gen-erate a nanoscale signature library. Although anecessary step, this alone was not sufficient toengineer an optimum few-photon FPM inter-action. A specific core fluctuation profile corre-sponding to the maximum pump depletionalso had to be identified. This was guided by acoupled-mode calculation (13) predicting thata strong (1.5 W) pump can be depleted by a100-nW signal if the gPL-product exceeds 10.The search for the optimum core variation wasconstrained by the requirement that the FPMoccurs in a fiber shorter than L ∼ 10/15 W−1 km−1/1 W ∼ 600 m, with the assumption of standardconfinement (g ∼ 15 W−1 km−1). The calculationresulted in a unique core variation profile thatindeed could be closely approximated by com-bining two distinct fiber sections from the corefluctuation library (Fig. 3).

Fig. 2. Four-photon mixing in fibers with nanometer-scale core variations. (A) Maximum parametric
gain in a homogeneous fiber is defined by the instantaneous pump power P. With pump depletion, the
gain peak shifts away from the signal S at frequency wS, preventing further pump-signal photon transfer.
The shaded area represents the magnitude of parametric gain. (B) By varying the core size, local phase
matching can be controlled to maintain the gain peak position even when the pump is depleted. (C) ER
calculated by the nonlinear Schrodinger model. Each point represents a unique core variation function.

Fig. 3. Photon switching in fiber with optimal core. (A) Calculated (dotted) and measured (solid) core
variation functions selected for few-photon switching experiments. Core variation is plotted as a deviation
from the mean core size. The unique core variation was created by combining two distinct fiber sections
identified from the measurement library; the splice was applied at z = 245.2 m. (B) Experimental
schematics for static and fast switching characterization. A CW laser (pump) was combined with
classically attenuated weak CW or pulsed signal and launched into the nonlinear fiber.